Question

what sum will become rs 4913 in 1½years if the rate of interest is 12½% compounded half yearly​

Answer 1

Given,

• $\text{Amount}\: (A)= ₹4913,$

Compounded Half Yearly At,

• $\text{Rate} \: (R) = 12 \: \frac{1}{2} \%,$
• $\text{For} \: 1 \: \frac{1}{2} \: \text{years}.$

To Find,

• The Principal.

Solution,

Given that,

• $A = ₹ 4913,$
• $R = 12 \: \frac{1}{2} \%,$

And,

• $T = 1 \frac{1}{2} \: \text{years}.$

Finding the Amount,

As we know,

• $\boxed{\text{Amount}_{(\text{Compounded Half Yearly)} }= P\bigg(1 + \frac{R}{200} \bigg)^{2T}}$

Substituting the values and Finding the Amount,

$:\longmapsto 4913 = P\bigg(1 + \frac{12 \frac{1}{2} }{200} \bigg)^{2 (1 \frac{1}{2}) } \\ \\ :\longmapsto 4913 = P \bigg(1 + \frac{ \frac{25}{2} }{200} \bigg)^{2 ( \frac{3}{2}) } \\ \\ :\longmapsto 4913= P\bigg(1 + \frac{25}{2 \times 200} \bigg) ^{3} \\ \\ :\longmapsto 4913 = P{ \bigg(1 + \frac{1}{16} \bigg) }^{3} \\ \\ :\longmapsto 4913 = P { \bigg( \frac{17}{16} \bigg) }^{3} \\ \\ :\longmapsto 4913 = P \times \frac{17}{16} \times \frac{17}{16} \times \frac{17}{16} \\ \\ :\longmapsto4913 = P \times \frac{4913}{4096} \\ \\ :\longmapsto P = 4913 \times \frac{4096}{4913} \\ \\ :\longmapsto \boxed{ \text{Principal} = ₹4096}$

Therefore,

• The Principal is ₹4096.

Required Answer,

• The Sum ₹4096 will becomes ₹4913 in 1 ½ Years If the Rate of interest is 12 ½ % Compounded Half Yearly.